HOW RAPIDLY AND HOW FAR DO NEUTRONS MIGRATE

Exact formulas are derived for the mean-squared displacements of neutr ons from an isotropic point, line, or plane source in an infinite homo geneous medium. These displacements depend on the initial energy Eo of the neutron, the elapsed time t since the birth of the neutron, and t he energy E(o) of the neutron at time t. Our results are stated in ter ms of the solutions of three infinite-medium transport equations - it is not necessary to solve a space-dependent transport equation, even t hough the underlying transport problem is space-dependent. Also, time and energy-dependent diffusion equations are formulated, whose diffusi on coefficients are chosen so that their solutions exactly preserve ce rtain of the mean-squared displacement properties of the transport equ ation.